The present invention relates generally to evaluations of optical elements, and particularly to a method of evaluating an optical element (e.g., a mirror) on which a multilayer coating is formed using a standing wave, as well as an optical element manufacturing method using such evaluation results and an optical apparatus using the optical element. The present invention is particularly suitable, for example, for evaluation and manufacturing of a multilayer mirror used for a projection exposure apparatus that uses exposure light with a wavelength of 2 to 40 nm to expose various devices such as semiconductor chips (e.g., ICs, LSIs, etc.), display devices (e.g., liquid crystal panels, and the like), sensing devices (e.g., magnetic heads, and the like), and image pickup devices (e.g., CCDs, and the like), as well as adjustments of an optical system having the optical element.
One conventional lithography means for manufacturing fine semiconductor devices such as semiconductor memories, and logic circuits is reduction projection exposure using ultraviolet light. However, the lithography using ultraviolet light has its limit as the semiconductor devices are rapidly becoming more and more fine. In order to efficiently expose so fine of a circuit pattern as less than 50 nm, there has developed an exposure apparatus that uses extreme ultraviolet (“EUV”) light with a wavelength shorter than that of the ultraviolet light (hereinafter called “an EUV exposure apparatus”), e.g., a wavelength of more or less 13.5 nm.
The EUV exposure apparatus uses a reflective optical element such as a mirror for its optical system, and forms a multilayer coating, which is made of reciprocally deposited two kinds of materials having different optical constants, on the surface of the reflective optical element. The multilayer coating laminates, e.g., molybdenum (Mo) and silicon (Si), one after the other, on the surface of a glass substrate that is polished to an accurate shape, with a 3 nm-thick Mo layer and a 4 nm-thick Si layer. A combined layer thickness of two kinds of materials is called a coating period. In the above example, the coating period is 7 nm.
Such a multilayer mirror, when receiving the EUV light, efficiently reflects the EUV light with a specific wavelength, i.e., only the EUV light that has a narrow bandwidth centering around and satisfies Bragg's condition. The interference condition is expressed using θ is an incident angle, λ is a wavelength of the EUV light, and d is the coating period. The bandwidth at that time is more or less 0.6 to 1 nm. The interference condition is approximately expressed by, but strictly speaking slightly offset due to influences of refractions in the materials, etc. from, a relational expression of the following Bragg's equation:2×d×cos θ=λ  (1)
A surface shape of a projection optical system's reflective surface should be made so precise that it meets, for example, a shape error budget σ (rms value) given in the Marechal's criterion, where n is the number of mirrors in a projection optical system, and λ is a wavelength of EUV light:σ=λ/(28×√n)  (2)For example, σ=0.19 nm for a six-mirror system with a wavelength of 13 nm. For a pattern transfer with a resolution of 30 nm, wave aberration tolerated to a total projection optical system is more or less 0.4 nm.
A manufacturing method of the projection optical system includes the steps of forming a multilayer mirror, measuring its shape, incorporating it into a barrel, and adjusting the wave aberration.
The multilayer mirror formation step, first, polishes a substrate while repeatedly measuring its shape with an interferometer that uses visible light so as to shape the substrate. Next, a multilayer coating is put onto the substrate surface to arrange an optimal coating thickness distribution with respect to angles and the wavelength of light entering the multilayer coating at various positions within the mirror surface for actual use of the optical system.
The shape measurement step measures the surface shape of the multilayer mirror just having finished the multilayer coating formation once again by an interferometer using the visible light, as well as determining whether the multilayer coating surface satisfies its designated shape (i.e., the above shape error σ). The multilayer mirror, which is found not to have an intended surface shape, is determined coating failed, and the multilayer coating is stripped off and re-formed.
The mirror barrel incorporation step incorporates into a mirror barrel the multilayer mirrors each determined in the shape measurement step to have the designated surface shape, and adjusts their mutual spacing and tilting, thus completing a projection optical system.
The wave aberration adjustment step adjusts a wave aberration of the projection optical system. If a phase change of light due to its reflection results in a constant value, a wavefront of light reflecting on a mirror can be calculated based on a wavefront of incident light and a mirror shape, but in reality, a phase change of light reflecting on the multilayer mirror differs depending on wavelength, incident angle of light, and coating structure. As a result, the measurements of a geometric surface shape by visible light cannot accurately provide a wavefront of the reflected EUV light. Accordingly, one limitedly implemented method uses the EUV light to directly measure a wavefront of the light reflected on a multilayer mirror or a projection optical system. For example, one known means for directly measuring the wavefront of the light reflective on the multilayer mirror by using the EUV light is a point diffraction interferometer (“PDI”) that uses a pinhole to produce a spherical wave (see, for example, Japanese Patent Applications, Publication Nos. 2001-227909 and 2000-97620).
Other prior art includes a method for obtaining information about a layer structure and interface roughness of an X-ray multilayer mirror from a shape of an X-ray standing wave spectrum (see, for example, Japanese Patent Applications, Publication Nos. 2002-243669 and 2000-55841).
Data on electron energy losses in a material is disclosed in “Stopping Power of Matter for Electrons below 10 keV” page 279 of Journal of Applied Physics Vol. 51, No. 3 (March, 1982) by Yohta Nakai, et al. As a relationship between reflectance and phases of reflected light on a multilayer coating, model calculations are disclosed in “Layered Synthetic Microstructures as Bragg's Diffractors for X-Rays and Extreme Ultraviolet: Theory and Predicted Performance” Applied Optics 20, 3027 (1981) by J. H. Underwood and T. W. Barbee. A photoelectric effect of a multilayer coating surface is disclosed in “Controlling contamination in Mo/Si multilayer mirrors by Si surface capping modifications” in pp. 442-453 of Proc. SPIE Vol. 4668 (July, 2002) by Michael E. Malinowski, Chip Steinhaus, W. Miles Clift, Leonard E. Klebanoff, Stanley Mrowka, and Regina Soufli.
However, the PDI method needs an optical system that converges light divergent from one point to another point, and cannot disadvantageously measure a convex surface. In addition, it has a difficulty in measuring even a concave surface when it is an aspheric surface that has a large aspheric volume. Therefore, this method cannot be applied to all the mirrors in the projection optical system, but can only be used for certain measurable mirrors in a limited way.
A relationship of wavefronts between the incident light and the reflected light cannot be actually measured for the remaining mirrors. Therefore, these mirrors can include wavefront aberrations, and a mirror barrel combining those mirrors may not possibly satisfy the intended optical performance. In addition, the PDI method also has a manufacturing problem in that a pinhole used to generate an accurate spherical wave is as small as to the order of several tens of nm. Moreover, a high intensity light source necessary to introduce an ample amount of EUV light into the small pinhole causes a large and expensive measurement system.
Japanese Patent Application, Publication No. 2002-243669 can measure a multilayer mirror's layer shape easily, but cannot obtain a wavefront of the reflected light without considering the phase. An inaccurately obtained wavefront of the reflected light provides the insufficient adjustment of the wavefront aberration, and the insufficient adjustment of the wavefront aberration cannot provide an intended resolution.
Therefore, the present invention has an exemplified object to provide an evaluation method for an optical element that makes it possible to accurately, simply, and inexpensively measure the shape of an optical element having an arbitrary shape that is observed from incident light, and a relationship between incident light and reflected light.